Base field 4.4.14197.1
Generator \(w\), with minimal polynomial \(x^{4} - 6x^{2} - 3x + 1\); narrow class number \(2\) and class number \(1\).
Form
| Weight: | $[2, 2, 2, 2]$ |
| Level: | $[31, 31, w^{3} - 6w - 1]$ |
| Dimension: | $5$ |
| CM: | no |
| Base change: | no |
| Newspace dimension: | $44$ |
Hecke eigenvalues ($q$-expansion)
The Hecke eigenvalue field is $\Q(e)$ where $e$ is a root of the defining polynomial:
| \(x^{5} - 15x^{4} + 82x^{3} - 193x^{2} + 164x + 2\) |
Show full eigenvalues Hide large eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| 7 | $[7, 7, w - 1]$ | $\phantom{-}e$ |
| 9 | $[9, 3, w^{3} - 5w - 2]$ | $\phantom{-}e^{4} - 12e^{3} + 46e^{2} - 56e + 1$ |
| 9 | $[9, 3, w^{3} - w^{2} - 4w]$ | $-e^{3} + 8e^{2} - 14e - 4$ |
| 13 | $[13, 13, -w + 2]$ | $-e + 3$ |
| 16 | $[16, 2, 2]$ | $\phantom{-}2e^{4} - 24e^{3} + 92e^{2} - 111e - 3$ |
| 17 | $[17, 17, w^{3} - w^{2} - 5w]$ | $-e^{3} + 8e^{2} - 15e - 2$ |
| 19 | $[19, 19, -w^{3} + w^{2} + 6w]$ | $-e^{3} + 9e^{2} - 20e + 5$ |
| 23 | $[23, 23, -w^{2} + w + 3]$ | $-e^{4} + 11e^{3} - 39e^{2} + 46e - 2$ |
| 29 | $[29, 29, w^{3} - 5w]$ | $-e^{4} + 11e^{3} - 38e^{2} + 38e + 6$ |
| 31 | $[31, 31, w^{3} - 6w - 1]$ | $-1$ |
| 31 | $[31, 31, w^{2} - 2]$ | $\phantom{-}2e^{4} - 23e^{3} + 86e^{2} - 107e + 8$ |
| 37 | $[37, 37, -w - 3]$ | $-e^{4} + 11e^{3} - 38e^{2} + 40e$ |
| 37 | $[37, 37, w^{3} - 4w - 1]$ | $-e^{4} + 12e^{3} - 45e^{2} + 52e + 1$ |
| 37 | $[37, 37, w^{3} - 7w - 4]$ | $\phantom{-}e^{4} - 12e^{3} + 47e^{2} - 57e - 8$ |
| 37 | $[37, 37, w^{2} - 3]$ | $\phantom{-}3e^{4} - 34e^{3} + 122e^{2} - 135e - 8$ |
| 43 | $[43, 43, w^{2} + w - 3]$ | $-2e^{4} + 21e^{3} - 68e^{2} + 65e + 2$ |
| 43 | $[43, 43, w^{3} - w^{2} - 5w - 1]$ | $\phantom{-}e^{4} - 11e^{3} + 37e^{2} - 37e$ |
| 47 | $[47, 47, -w^{3} + w^{2} + 5w - 4]$ | $\phantom{-}e^{3} - 6e^{2} + 5e + 5$ |
| 53 | $[53, 53, w^{3} - 6w]$ | $\phantom{-}2e^{4} - 22e^{3} + 77e^{2} - 85e + 6$ |
| 61 | $[61, 61, w^{3} - w^{2} - 7w - 2]$ | $\phantom{-}e^{3} - 9e^{2} + 20e$ |
Atkin-Lehner eigenvalues
| Norm | Prime | Eigenvalue |
|---|---|---|
| $31$ | $[31, 31, w^{3} - 6w - 1]$ | $1$ |